Problem: $-10ij + 8j + 9k - 6 = 5j - 10k + 7$ Solve for $i$.
Answer: Combine constant terms on the right. $-10ij + 8j + 9k - {6} = 5j - 10k + {7}$ $-10ij + 8j + 9k = 5j - 10k + {13}$ Combine $k$ terms on the right. $-10ij + 8j + {9k} = 5j - {10k} + 13$ $-10ij + 8j = 5j - {19k} + 13$ Combine $j$ terms on the right. $-10ij + {8j} = {5j} - 19k + 13$ $-10ij = -{3j} - 19k + 13$ Isolate $i$ $-{10}i{j} = -3j - 19k + 13$ $i = \dfrac{ -3j - 19k + 13 }{ -{10j} }$ Swap the signs so the denominator isn't negative. $i = \dfrac{ {3}j + {19}k - {13} }{ {10j} }$